Measurement condition in simulations.
Tissue harmonic imaging (THI) is highly effective for correct diagnosis. On the other hand, pulse compression is often used in a radar system and an ultrasound imaging system to perform high SNR measurement. Therefore, the performance of pulse compression of tissue harmonic imaging is required to be improved. The frequency-dependent attenuation (FDA) is a crucial problem in medical tissue imaging. In the pulse compression imaging, the deterioration of echoes by the FDA lowers the performance of a matched filtering using an ideal transmitted pulse as a template signal. Since, especially in the harmonic imaging, higher-frequency components are used for imaging than the fundamental imaging, the compensation of the FDA is strongly important for high-definition imaging. In this study, we examine a method to reduce the influence of the FDA on harmonics.
- pulse compression
- tissue harmonic imaging
- FM chirp
- compensation for FDA
The ultimate goal of our study is to perform high-resolution and high signal-to-noise ratio (SNR) ultrasound imaging required for high-quality diagnosis. Such imaging is strongly demanded particularly in the deep part of a living body. On the other hand, we are developing a puncture ultrasound microscope [1, 2, 3], in which echo is very weak and cell-level resolution is required, so high-definite imaging technique is absolutely important. A pulse compression technique (PCT) is effective for improving SNR while maintaining safety to the living body [4, 5, 6].
In PCTs, broadband modulation is necessary to improve the range resolution. The bandwidth that is used efficiently for transmission and reception is limited by the resonance characteristics of the transducer that utilizes thickness resonance vibration. In order to widen the bandwidth of the transducer, a layered-type transducer has been developed in which two piezoelectric oscillators having different thicknesses are longitudinally bonded and one of a pair of electrodes is inserted between two oscillators . In addition, we are proposing the concept of a new transducer based on a PMUT structure with a thicker diaphragm than conventional PMUT and by which the bandwidth can be greatly widened . In general, the wide bandwidth of the transmitted pulses is a prerequisite for sharp pulses. Therefore, broadband transmission in PCTs improves range resolution. On the other hand, in order to improve the SNR by PCTs, it is necessary to increase energy inflow into the body by transmitting a signal with a wide pulse width. Namely, a PCT using pulses having a wideband and a wide pulse width is suitable for our objective.
Due to its high resolution, tissue harmonic imaging (THI) is useful, and many studies have been done [9, 10]. THI uses harmonic components generated as nonlinear distortion caused by ultrasonic propagation in living tissue for imaging. In a commercial implement, the second harmonic component is generally used since its amplitude is drastically greater than the amplitude of the higher-order harmonic components. The advantages of THI can be summarized as follows: (i) THI has high-resolution characteristics along the range direction compared to fundamental imaging due to the broadband characteristics of the harmonic components, (ii) THI has high-resolution characteristics along the azimuth direction since the nonlinear effect strongly occurs at the center of the transmitted beam with high sound pressure, and (iii) there are almost no artifacts such as multiple reflection and side lobes in THI since the sound pressure of the echo reflected from the scatterer is low and hence the sound pressure of the multiple reflected echo is further low, and the amplitude of the side lobes of harmonics is 60–80 dB smaller than that of the main lobe. On the other hand, in THI the amplitude of the harmonic components is significantly smaller than the amplitude of the fundamental component. In order to solve this problem, we proposed a method based on the Bayesian estimation using the prior information of the second harmonic echoes introduced from fundamental echoes .
Applying a PCT to THI is expected to improve the SNR while maintaining high-resolution characteristics, but frequency-dependent attenuation (FDA) must be strongly aware. FDA causes severe distortion of echo signals, when the broadband pulse propagates through the soft tissue in the living body. Since the high-frequency component attenuates more than the low-frequency component, particularly large distortion occurs in harmonic components. Figure 1 shows the FDA in the time domain and Figure 2 shows it in the frequency domain. The distortion of the echo caused by FDA makes exact pulse compression impossible, and, hence, image blurring occurs . In order to prevent the SNR degradation and of the range resolution degradation due to the echo distortion caused by FDA, we have proposed an FDA compensation method [12, 13, 14]. In the methods, an amplitude-modulated FM chirp pulse is transmitted, the echo for which is distorted by FDA and, as a result, is received as an ideal waveform. The proper amplitude modification (AM) of the transmission is determined using the FDA characteristic measured by transmitting a reference pulse toward a region of interest (ROI) and receiving the corresponding echo. Since the methods proposed [12, 13] have been constructed for fundamental imaging, this study aims to extend them for THI imaging. The method  was constructed for harmonic imaging, but the compensation of the transducer characteristics was insufficient, which will be solved in this study to propose an FDA compensation method with high completeness. Typical purposes of AM of an FM chirp signal are side-lobe suppression and compensation of the resonance characteristics of a transducer . The techniques for these purposes can be also integrated into our method. The effectiveness of our method on the harmonic FDA compensation is confirmed through numerical simulations by finite element method (FEM) and simple experiments.
2.1. Transducer characteristic compensation
2.1.1. Compensation for fundamental band
Before considering FDA compensation, it is necessary to correct the frequency characteristic of the transducer, which must be done only once for each transducer. For fundamental imaging, the transmission and reception characteristics of the transducer are simply compensated for both amplitude and phase. To evaluate the characteristic, any arbitrary FM chirp signal
In this equation,
The simulation confirmed that beam focusing has little effect on measuring transducer characteristics.
2.1.2. Compensation for fundamental transmission and harmonic reception
For tissue harmonic imaging, the transmission characteristic in the fundamental frequency band and the reception characteristic in the harmonic frequency band must be corrected at the same time. That is, the harmonic echo is distorted due to the fundamental transmission characteristic and the harmonic reception characteristic. Hereafter, attention is focused only on the second harmonic component. The fundamental transmission characteristic can be evaluated by experimentally measuring the transmitted pressure by a hydrophone. We represent an arbitral FM chirp transmission signal
In addition, the inverse mapping is also defined as follows:
These mapping functions can simply be determined by scaling and shifting the corresponding components on the frequency axis. The scale factor between
Using these definition and the harmonic pressure
As the transmitted fundamental pulse propagates toward the ROI, harmonics are gradually generated, and such a detailed process is ignored in the derivation of the above equation. To generate the time signal
2.2. FDA compensation
2.2.1. Method for fundamental component
FDA compensation can be performed basically in the same way as compensating the characteristics of the transducer. However, it is noted that the FDA compensation should be carried out for each region of interest (ROI) that is required to be finely imaged. To estimate the distortion characteristics caused by FDA in the propagation medium, as a reference transmission for investigation, we transmit
By using this, the transmission signal
The definition of
2.2.2. Method for harmonic component
Therefore, the transmission signal
It should be noted that the FDA within the fundamental band only occurs in the outbound path from the transducer to the reflective target. However, since the scale factor as a constant independent of the frequency does not affect the distortion of the waveform, |
The amplitude-modulated FM chirp pulse
3.1. Simulation condition for transducer characteristic compensation
The simulations in this study were performed using PZFlex (Weidlinger Associates, Inc.), which is a standard finite element method (FEM) simulator for ultrasound propagation and piezoelectric analysis. A two-dimensional simulation model for determining a transmission signal that compensates transducer characteristics is shown in Figure 4. A linear array transducer having 64 oscillating elements of PZT was assumed, and an iron plate was used as a reflector. Parameters of the transmission signal is shown in Table 1. To evaluate the characteristics of the transducer purely, FDA should not occur, so the attenuation coefficient of water is set to 0 dB/cm/MHz. The transmission pulse is focused on the front face of the iron plate. The characteristics of the transducer and the signal compensating for it can be confirmed from the simulation results already shown in Figure 3 in Section 2.1.2.
3.2. Definition of FDA model
In the PZFlex, the definition of FDA is represented as
3.3. Simulation condition for FDA compensation
It is necessary to confirm the effectiveness of our method under medical usage condition assuming a living body. Since it is difficult to verify such effectiveness from the beginning through experiments, two-dimensional FEM simulations were performed using a model shown in Figure 5 in which the propagation medium imitates the liver and the object corresponds to a tumor. Transmission pulses are formed in the same way as the simulations in Section 3.1 and are focused on 30 mm away from the transducer, i.e., on the front of the target object. Parameters of the transmission signal are also the same as in Table 1 in Section 3.1. The medium in Figure 5 consists of scatterers that can mimic the speckle patterns of the liver. Sound speed, density, and attenuation coefficient of each scatterer are randomly defined within the range of Table 2. The blue object shown in Figure 5 mimics the tumor, and its properties are also shown in Table 2. We simulate the echoes reflected from the front of the object and analyze them.
|Type of transmission signal||FM chirp with Hanning window|
|Center frequency [MHz]||10|
|Frequency bandwidth [MHz]||4|
|Pulse duration [μm]||5|
|Focus of transducer [mm]||15|
|Sampling frequency [MHz]||500|
|Transmission voltage [V]||40|
|Number of oscillator elements||64|
|Medium||Sound speed [m/s]||Density [kg/m3]||Attenuation coefficient [dB/cm/MHz]||Nonlinear parameter [B/A]|
3.4. Results of harmonic FDA compensation
The absolute values of
Figure 8(a) shows the second harmonic component of the echo from the object in Figure 5 without FDA compensation, i.e., the echo corresponds to
4.1. Experimental setup
In order to confirm the actual effectiveness of our FDA compensation, we conducted simple experiments using the experimental system shown in Figure 13(a). The transducer used in the experiments shown in Figure 13(b) is SONIX ISI506R having a center frequency of 5 MHz. The amplifier is Amplifier Research 50A15, the function generator is Tektronix APG3102, and the oscilloscope is IWATSU DS-5552. A linear FM chirp signal was transmitted toward the iron plate placed 15 cm away from the transducer, and the echo reflected from the iron plate was observed. The measurement conditions are shown in Table 3. Experimental verification of the characteristics of the transducer can be realized by measurement of transmitted sound pressure in water by a hydrophone. In this issue, we focused on confirming the effect of FDA compensation and conducted experiments using frequency bands with relatively flat transducer characteristics. Hence, in the experiments, the characteristics of the transducer were not taken into account, and only the FDA of water was compensated. That is, instead of
|Type of transmission signal||FM chirp with Hanning window|
|Center frequency [MHz]||7.5|
|Frequency bandwidth [MHz]||3|
|Pulse duration [μm]||10|
|Focus of transducer [mm]||15|
|Sampling frequency [MHz]||500|
|Transmission voltage [V]||40|
4.2. Experimental results
In this section, the experimental results of our method for compensating FDA in the second harmonic band caused by water corresponding to a sufficient propagating distance are shown. Figure 14(a) shows the experimentally measured echo reflected from the iron plate without FDA compensation. Figure 14(b) shows the second harmonic echo extracted from the whole echo of Figure 14(a), and its spectrum amplitude is shown in Figure 14(c). In the high-frequency part in Figure 14(c), the FDA of the second harmonic component is seen. By transmitting a reference signal and estimating |
In this study, we proposed a novel and simple method for FDA compensation to realize the fine THI, which can also compensate transducer characteristics. Its effectiveness was confirmed by two-dimensional simulations using a model imitating liver and tumor and by simple experiments. Our method is based on FM chirp pulse compression to realize high SNR, and we expect that fine imaging is effectively performed in a local manner by setting a ROI determined by preimaging by conventional B-mode imaging. In this study, investigation of FDA characteristics is assumed to be performed locally by transmitting a reference signal and receiving its echo position to be finely imaged. However, it can be considered that such FDA characteristics are invariant in the tissue region having uniform characteristics. This indicates that it is possible to reduce the number of transmission and reception for reference and it becomes easy to obtain the whole high-definition imaging. In the future, we will examine such an extended method and conduct the experiments using a phantom that imitates a living body and also the experiments on living tissue.
In the research field of ultrasound harmonic imaging, mainly the method of extracting the harmonic component appropriately from the echo  and the technique to increase the noise resistance of the harmonic component  are extensively examined. As sound pressure is higher, large harmonic components are generated, so sharp transmission pulses are generally used in many studies in general. In our study, from the viewpoint of using more energy, we aim to improve the SNR of the harmonic components by using FM chirp pulses, and FDA compensation is important for PCT in order to avoid deterioration of the waveform after compression processing. We are studying a method to enable super resolution by multiple transmission and reception with different carrier frequencies , and FDA compensation is also important for applying this method to harmonic components.
A part of this work was supported by JSPS KAKENHI Grant Number 25350569.